X alone can complete a piece of work in 40 days. He worked for 8 days and left. Y alone completed the remaining work in 16 days. How long would X and Y together take to complete the work ?

Explanation:

Let total work = 40 units

(TW)40−→−1 units/day40days(X)

X’s 1 day work = 1 unit

X’s 8 days work is 8×1=8 units

Work left =40−8=32 work

left32−→−2 units/day16days(Y)

Y’s one day work = 2 units

X’s one day work = 1 unit

(X+Y) complete the whole work together in =40\ 2+1=13 1\3 days